Use the image to answer the question.
An illustration shows a 10 by 10 grid. A non-right triangle is enclosed within the grid. The first vertex is at the top of row 3 and the right of column 3. The second vertex is at the bottom of row 10 and the left of column 1. The third vertex is at the bottom of row 10 and the right of column 10.
What is the area of the non-right triangle? The base and height are found by counting the squares.
(1 point)
The area of the non-right triangle is 49 square units.
To find the area of the non-right triangle, we need to first determine the base and height of the triangle by counting the number of squares.
From the information given, we can see that the base of the triangle is the horizontal side formed by connecting the first and third vertices. Counting the squares, we can see that the base has a length of 10 - 1 = 9 squares.
The height of the triangle is the vertical side formed by connecting the second vertex with the base. We count the squares to see that the height of the triangle is 10 - 3 = 7 squares.
Now that we have the base and height, we can use the formula for the area of a triangle: Area = (base * height) / 2.
Plugging in the values, we have:
Area = (9 * 7) / 2
= 63 / 2
= 31.5 squares.
Therefore, the area of the non-right triangle is 31.5 squares.
To find the area of the non-right triangle within the grid, we need to calculate the base and height of the triangle in terms of the number of squares.
First, let's find the base of the triangle. We start at the top of row 3 and the right of column 3, and move to the bottom of row 10 and the left of column 1.
To find the number of squares in the base, we need to count the number of vertical squares between these two points. From the top of row 3 to the bottom of row 10, there are 10 - 3 + 1 = 8 rows. So the number of vertical squares in the base is 8.
Next, let's find the height of the triangle. We start at the bottom of row 10 and the right of column 10, and move to the bottom of row 10 and the left of column 1.
To find the number of squares in the height, we need to count the number of horizontal squares between these two points. From the right of column 1 to the right of column 10, there are 10 - 1 + 1 = 10 columns. So the number of horizontal squares in the height is 10.
Now, we can calculate the area of the triangle. The area of a triangle is given by the formula: Area = (1/2) * base * height.
In this case, the base is 8 squares and the height is 10 squares. Plugging these values into the formula, we get:
Area = (1/2) * 8 * 10
= 4 * 10
= 40 square units.
Therefore, the area of the non-right triangle within the grid is 40 square units.